A278008 Number of n X 2 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 6, 30, 198, 1230, 7734, 48510, 304422, 1910190, 11986326, 75213150, 471956358, 2961486990, 18583085814, 116607324990, 731701311462, 4591365157230, 28810436277846, 180783102647070, 1134399003458118, 7118259838467150

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-1) + 8*a(n-2).

Conjectures from Colin Barker, Feb 07 2019: (Start)

G.f.: 6*x^2 / (1 - 5*x - 8*x^2).

a(n) = 2^(-3-n) * ((57-5*sqrt(57))*(5+sqrt(57))^n + (5-sqrt(57))^n*(57+5*sqrt(57))) / 19.

(End)

Example

Some solutions for n=4:
..0..1. .0..2. .0..1. .0..1. .0..1. .0..1. .0..1. .0..2. .0..2. .0..2
..0..2. .1..2. .0..2. .0..2. .0..2. .2..2. .1..2. .1..1. .1..1. .1..0
..2..1. .2..0. .2..0. .1..2. .1..2. .1..1. .0..1. .0..1. .0..2. .2..1
..2..0. .2..1. .1..1. .0..0. .1..1. .0..2. .0..0. .2..2. .1..1. .0..1

Crossrefs

Column 2 of A278014.

Sequence in context: A147517 A294221 A005922 * A370751 A325950 A275953

Adjacent sequences: A278005 A278006 A278007 * A278009 A278010 A278011

Keyword

nonn

Author

R. H. Hardin, Nov 08 2016

Status

approved